Method for estimating the frequency shift of a CPFSK signal

ABSTRACT

A method for estimating the frequency shift of a CPFSK signal includes scanning the CPFSK signal. Intermediate signal values are determined for the scanned CPFSK signal. An estimated value (ν) is determined for the frequency shift of the CPFSK signal by assessing a predefined number of L 0  consecutive intermediate signal values. An integer delay parameter D is specified. Intermediate signal values for intervals k·T+τ are determined in each case from scanning values of the CPFSK signal obtained for intervals k·D·T+τ and [k−1]·D·T+τ, whereby T designates a scanning period of the scanned CPFSK signal, k is a scanning index and τ is a delay constant. The estimated value (ν) for the frequency shift is determined from the intermediate signal values for intervals i·D·T+τ with i=0 . . . L 0 −1. The integer delay parameter D is variable and is selected depending on the type of CPFSK modulation used for the CPFSK signal.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to an estimation method, and more specifically toa method for estimating the frequency shift of a CPFSK signal.

2. Description of the Related Art

Digital receiver systems for frequency or phase modulated signals, inparticular for CPFSK signals (“Continuous Phase Frequency Shift Keying”)frequently also requite, for correct and highly efficient detection ofthe transmitted symbols, apart from symbol synchronisation, digitalestimation and correction of a possible phase or frequency shift.

For the purpose of estimating the frequency shift intuitive methods areused which employ known signal characteristics or characteristics fromsignals derived from the incoming signal, as well as methods which arebased on the so-called ML principle (“Maximum Likelihood”). In this casebasically a distinction is made between data-aided and non-data-aided aswell as clock-aided and non-clock-aided methods. In addition adistinction can be made between estimating methods without feed back(feed forward or open loop) and estimating methods with feed back(closed loop).

In “Synchronisation Techniques for Digital Receivers” U. Mengali and A.N. D'Andrea, Plenum Press, New York, 1997 a number of known methods forestimating the digital frequency shift are described whereby inparticular a non-data-aided, though clock-aided estimating method forMSK signals (“Minimum Shift Keying”) is presented, which relies on theso-called “Delay and Multiply” principle. A differential demodulator isused as an essential component in this case. This known method will beexplained below in more detail.

With this known method it is firstly assumed that an MSK incoming signalr(t) is filtered for noise limitation and the resultant filtered MSKincoming signal x(t) is scanned at predetermined intervals kT+τ, wherebyk designates the scanning index, T the symbol duration of the incomingsignal and τ a delay constant. As described in more detail in“Synchronisation Techniques for Digital Receivers”, U. Mengali and A. N.D'Andrea, Plenum Press, New York, 1997, an intermediate signal z(k·T+τ)can be derived from the filtered and scanned complex envelope x(k·T+τ)of the incoming signal (as well as the corresponding conjugated complexsignal x*(k·T+τ)) as follows:z(k·T+τ)=x ²(k·T+τ)·{x ²([k−1]·T+τ)}*={x(k·T+τ)·x*([k−1]·T+τ)}²

This intermediate signal gives the estimated value for the frequencyshift ν by assessing an observation interval including L₀ receiversymbols:

$v = {{{{- \frac{1}{4\pi\; T}} \cdot \arg}\{ {{z(\tau)} + {z( {T + \tau} )} + {z( {{2 \cdot T} + \tau} )} + \;{.\;.\;.\;{+ {z( {{\lbrack {L_{0} - 1} \rbrack \cdot T} + \tau} )}}}} \}} = {{{- \frac{1}{4\pi\; T}} \cdot \arg}\{ {\sum\limits_{k = 0}^{L_{0} - 1}\;{z( {{k \cdot T} + \tau} )}} \}}}$

As already mentioned, the method described above however concerns amodel developed for MSK incoming signals. During MSK modulation thecarrier phase during the time T of a symbol is rotated around the amount

${\pm \frac{\pi}{2}},$so that the frequency of the transmitted signal, dependent on the symbolbeing transmitted, changes between

$\varpi_{0} + \frac{\pi}{2 \cdot T}$and

${\varpi_{0} - \frac{\pi}{2 \cdot T}},$whereby ω₀ designates the nominal carrier frequency.

In the case of angle-modulated signals the phase of the carrier signalis changed in harmony with a phase function q(t) of a suitable phasefilter. For MSK signals the phase function is defined as follows:

${q(t)} = \{ \begin{matrix}0 & {t < 0} \\\frac{t}{T} & {0 \leq t < T} \\1 & {t > T}\end{matrix} $

The phase function q(t) therefore assumes its end value after theduration T of a transmitted symbol.

CPFSK signals however generally possess a phase function, in contrast toMSK signals, which only reach their end value after an interval of timeL·T where L>1, that is to say the phase function q(t) for CPFSK signalsis defined as follows:

${q(t)} = \{ \begin{matrix}0 & {t < 0} \\{q(t)} & {0 \leq t < {L \cdot T}} \\1 & {t > {L \cdot T}}\end{matrix} $

BRIEF SUMMARY OF THE INVENTION

The aim of this invention, based on the state of the art describedabove, is to provide for CPFSK signals a generally valid method toestimate frequency shift.

The features of the present invention will become more fully apparentfrom the following description, or may be learned by the practice of theinvention as set forth hereinafter.

According to the invention to estimate the frequency shift of a CPFSKsignal an integer delay parameter D is introduced which can be suitablyadjusted depending on the type of the CPFSK signal or the type ofmodulation selected in each case.

The CPFSK signal is scanned at intervals k·T+τ, whereby T designates thescanning period, k a scanning index and τ a delay constant. Intermediatesignal values in each case are calculated from the scanning values ofthe CPFSK signal obtained for the intervals k·D·T+τ and [k−1]·D·T+τ. Theestimated value for the frequency shift is then obtained from a numberof L₀ intermediate signal values that have previously been determinedfor the intervals i·D·T+τ (i= . . . L₀−1).

In particular the estimated value for the frequency shift can beobtained by calculation of the expression

${{\frac{1}{4 \cdot \pi \cdot D \cdot T} \cdot \arg}\{ {\sum\limits_{i = 0}^{L_{0} - i}\;{z( {{i \cdot D \cdot T} + \tau} )}} \}},$whereby z(i·D·T+τ) designates the intermediate signal value obtained forthe interval i·D·T+τ.

The estimating method according to the invention is generally valid forCPFSK signals and is also to be implemented favourably as regardscomplexity. Furthermore very good estimation results can also beachieved for short observation periods, that is to say for minimum L₀values

The invention is explained in more detail below with reference to theattached drawing.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows the principal structure of an arrangement to estimatefrequency shift of a signal, and

FIG. 2 to highlight the advantages of this invention shows anillustration of the mean frequency shift estimated using a methodaccording to the invention in comparison to the actual frequency shift.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

An arrangement to estimate the frequency shift or frequency offset ν ofa signal r(t) received by a digital receiver is illustrated in FIG. 1.

Since the incoming signal r(t), apart from a wanted portion, also has anoise portion, the incoming signal r(t) is initially passed through anantialiasing filter 1 which is usually in the form of a low-pass filter,in order to suppress the noise as far as possible. The filtered incomingsignal x(t) resulting is then scanned in a device 2 with a clock 1/T anda delay constant τ. From the filtered and scanned incoming signal x(k)an intermediate signal z(k) is then obtained with the aid of a device 3functioning as a differential modulator which is used as the basis forestimating the frequency shift v by an estimating device 4.

The method used by the estimating device 4 to estimate the frequencyshift will be explained in more detail below.

Although the incoming signal r(t) has been passed through the filter 1in order to suppress noise, the resulting filtered incoming signal x(t),apart from its wanted portion, also has a residual noise portion. Forthe complex envelope of the filtered and scanned incoming signaltherefore:x(k·T+τ)=s(k·T+τ)+n(k·T+τ)applies.

In this case s(k·T+τ) designates the wanted signal portion and n(k·T+τ)the residual noise portion. The wanted signal portion s(k·T+τ) of acomplex CPFSK signal is defined as follows:

${s( {{k \cdot T} + \tau} )} = {{\mathbb{e}}^{j{\lbrack{{2 \cdot \pi \cdot v \cdot {({{k \cdot T} + \tau})}} + \theta}\rbrack}} \cdot \sqrt{\frac{2 \cdot E_{h}}{T}} \cdot {\mathbb{e}}^{f\;{\psi{({{k \cdot 1},{< \alpha_{k} >}})}}}}$

In this case ν designates the frequency shift being estimated while θrepresents an unknown phase shift. In addition E_(b) designates the bitenergy of each transmitted bit and ψ(k·T,<α_(k)>) the phase angle at theinterval k·T. The phase angle is dependent on the phase changes α_(i)allocated to each transmitter symbol and the modulation index η asfollows:

${\psi( {{{k \cdot T},}{< \alpha_{k} >}} )} = {\pi \cdot \eta \cdot {\sum\limits_{l = 0}^{k - 1}\;\alpha_{i}}}$

The intermediate signal z(k·T+τ) is determined in the following way fromthe scanned complex envelope x(k·T+τ) and its conjugated complexenvelope x*(k·T+τ), whereby for CPFSK signals a delay parameter D isintroduced, which for example in the case of MSK signals has the valueD=1:z(k·T+τ)=x ²(k·D·T+τ)·{x ²([k−1]·D·T+τ)}*={x(k·D·T+σ)·x*([k−1]·D·T+τ)} ²

Over an observation period with L₀ values of the intermediate signalz(k·T+τ) obtained in this way the estimated frequency shift ν:

$\begin{matrix}{v = {{\frac{1}{4 \cdot \pi \cdot D \cdot T} \cdot \arg}\{ {{z(\tau)} + {z( {{D \cdot T} + \tau} )} +} }} \\{ {{z( {{2 \cdot D \cdot T} + \tau} )} + \;{.\;.\;.\;{+ {z( {{\lbrack {L_{0} - 1} \rbrack \cdot D \cdot T} + \tau} )}}}} \}} \\{= {{\frac{1}{4 \cdot \pi \cdot D \cdot T} \cdot \arg}\{ {\sum\limits_{i = 0}^{L_{0} - 1}\;{z( {{i \cdot D \cdot T} + \tau} )}} \}}}\end{matrix}$results.

By introducing the delay parameter D a generally valid formula for CPFSKsignals is thus obtained to estimate the frequency shift ν. Forestimating the frequency shift ν of a CPFSK signal (L>1) a possiblevalue of the delay parameter D is for example D=L, whereby L equals thenumber of symbols until the corresponding phase function q(t) hasreached its end value (compare the above statements).

In FIG. 2 the mean frequency shift ν estimated using the methodaccording to the invention is recorded in comparison to the actualfrequency shift f_(offset). This concerns the results of a simulationcarried out for a GMSK signal (“Gaussian Minimum Shift Keying”) with asignal to noise distance of 12 dB and a modulation index of η=0.5. Thefilter 1 had a bandwidth of B·T=0.5 while the value D=3 was selected forthe delay parameter. Further, to estimate the frequency shift ν anobservation interval of the length L₀=32 was assumed. It can be seenfrom the illustration in FIG. 2 that very good estimation results canalso be achieved for relatively short observation periods.

The estimating method according to the invention can be simplyimplemented for example with the aid of a mat-lab function designatedbelow as “DM_CA_Frequency”, which is called up with the parameters x, T,D and L₀ and as a result f produces the estimated value for thefrequency shift:function[f]=DM _(—) CA _(—) Frequency(x,T,D,L0)z=(x(1:D:L0).*conj(x(1+D:D:L0+D))). □2;f=−angle)(−sum(z))/(4*pi*D*T);

Within the function first the help variable z of the differentialmodulator or the device 3 (compare FIG. 1) is defined, before theestimated value for the frequency shift is finally obtained from it by asummation over L₀ values of the help variable z.

1. A method for estimating the frequency shift of a continuousphase-frequency-shift keying (CPFSK) signal, comprising the steps of: a)scanning the CPFSK signal; b) determining intermediate signal values forthe CPFSK signal scanned in step a); and c) determining an estimatedvalue (v) for the frequency shift of the CPFSK signal by assessing apredefined number of L₀ consecutive intermediate signal values obtainedin step b), whereby an integer delay parameter D is specified, wherebyin step b) the intermediate signal values for intervals k·T+τ aredetermined in each case from scanning values of the CPFSK signalobtained for intervals k·D·T+τ and [k−1]·D·T+τ, whereby T designates ascanning period, with which the CPFSK signal is scanned in step a), k isa scanning index and τ is a delay constant, and whereby in step c) theestimated value (ν) for the frequency shift is determined from theintermediate signal values thus obtained in step b) for intervalsi·D·T+τ with i=0 . . . L₀−1, wherein the integer delay parameter D isvariable and is selected depending on the type of CPFSK modulation usedfor the CPFSK signal.
 2. The method according to claim 1, wherein theCPFSK signal x(k·T+τ) scanned in step a) is present in complex form, andwherein the intermediate signal values z(k·T+τ) of step b) aredetermined according to the equationz·(k·T+τ)={x(k·D·T+τ)·x([k−1]·D·T+τ)}², whereby x* designates theconjugated complex form of the CPFSK signal, and wherein the estimatedvalue ν for the frequency shift is determined according to the equation$v = {{\frac{1}{4 \cdot \pi \cdot D \cdot T} \cdot \arg}{\{ {\sum\limits_{i = 0}^{L_{0} - 1}\;{z( {{i \cdot D \cdot T} + \tau} )}} \}.}}$3. The method according to claim 1, wherein the phase of the CPFSKsignal during its modulation is changed in harmony with a predeterminedphase function, the phase function reaches its end value after apredetermined number L of symbols of the CPFSK signal, and the value D=Lis selected for the delay parameter.
 4. The method according to claim 3,whereby the phase function allocated to the CPFSK signal is such thatL>1 applies.
 5. The method according to claim 1, further comprising thestep of passing the CPFSK signal through a low-pass filter before beingscanned in step a).
 6. The method according to claim 1, wherein theCPFSK signal is a transmitted signal sent over a digital mobile radiosystem, and the step of determining the estimated frequency shift (ν) ofthe CPFSK signal is carried out in a receiver of the digital mobileradio system, in order to correct the incoming CPFSK signal accordingly,depending on the estimated frequency shift (ν).